It sounds more like a people issue than a tech issue. I would try to take a gentle approach, and try to steer towards in ears, for his, and really everyone's benefit.
Maybe try introducing using the ear buds by getting him a pair of good IEM's, and letting him just use them at home for personal use. The basic single driver ones might not cut it here. Let him get used to having them in his ears, and also let him get used to how good the music sounds in them. Hopefully he'll want to achieve that level of fidelity when he's leading worship, and will be more open to using them on stage.
I've had this scenario dozens of times, and it comes down to how willing he's going to be wanting to improve the situation. He has to really understand the "why" behind the change. Also, if you're the one guiding this, be prepared, and be willing to spend a lot of extra time with this person to make sure you can make him as comfortable as possible going through this transition. It might take one on one time getting his voice, and his guitar sounds as close as you can in the IEM's that he's used to having on stage. Mic placement on guitar amps are critical for this, and it's going to be a lot of trial and error.
Setting up the IEM's stereo will also make a world of difference. You'll be able to demonstrate how well he can separate different instruments in his mix, instead of the sludge that he's fighting on stage now. Clarity like he can't even imagine can be achieved. Don't let him do one in ear, one ear out. That will only further the problems, and risk further damage to the ear that has the IEM in.
Don't try to work this out on Sunday morning rehearsals, that's not the time for that back and forth. I hope you're doing rehearsals during the week, if you're not, try to get some together for a short season to move this process along. Spend weekly rehearsals during the week to work on the tech, and let Sunday be focused on Sunday.
I hope this helps!
